Numerical analysis preprints, 2011–2021

2021:

  1. NA2021/01: Arieh Iserles, Karolina Kropielnicka, Katharina Schratz & Marcus Webb, "Solving the linear semiclassical Schrödinger equation on the real line"

2020:

  1. NA2020/03: Arieh Iserles, Karen Luong & Marcus Webb, "Approximation of wave packets on the real line"
  2. NA2020/02: Arieh Iserles & Marcus Webb, "A differential analogue of Favard's theorem"
  3. NA2020/01: Georg Maierhofer, Arieh Iserles & Nigel Peake, "An extended Filon–Clenshaw–Curtis method for high-frequency wave scattering problems in two dimensions"

2019:

  1. NA2019/03: Arieh Iserles & Marcus Webb, "A family of orthogonal rational functions and other orthogonal systems with a skew-Hermitian differentiation matrix"
  2. NA2019/02: Marissa Condon, Arieh Iserles, Karolina Kropielnicka & Pranav Singh, "Highly oscillatory time-dependent trapped wave equation"
  3. NA2019/01: Arieh Iserles & Marcus Webb, "Fast computation of orthogonal systems with a skew-symmetric differentiation matrix"

2018:

  1. NA2018/04: Jing Gao, Arieh Iserles & Marissa Condon, "Spectral computation of highly oscillatory integral equations in laser theory"
  2. NA2018/03: Arieh Iserles, Karolina Kropielnicka & Pranav Singh, "Compact schemes for laser-matter interaction in Schrödinger equation"
  3. NA2018/02: Arieh Iserles & Marcus Webb, "Magnus–Lanczos methods with simplified commutators for the Schrödinger equation with a time-dependent potential"
  4. NA2018/01: Arieh Iserles, Karolina Kropielnicka & Pranav Singh, "Magnus–Lanczos methods with simplified commutators for the Schrödinger equation with a time-dependent potential"

2017:

  1. NA2017/01: Arieh Iserles & Shev Macnamara, "Magnus expansions and pseudospectra of master equations"
  2. NA2017/02: Helge Dietert & Arieh Iserles, "Fast approximation on the real line"
  3. NA2017/03: Marissa Condon & Arieh Iserles, "Time-domain modelling of interconnects with highly oscillatory sources"
  4. NA2017/04: M.D. Buhmann, R. Fletcher, A. Iserles & P. Toint, "Michael J.D. Powell, 29 July 1936–19 April 2015"
  5. NA2017/05: Arieh Iserles, Karolina Kropielnicka & Pranav Singh, "Commutator-free Magnus–Lanczos methods for the linear Schrödinger equation"

2016:

  1. NA2016/01: C. Liu, A. Iserles & X. Wu, "Symmetric and arbitrarily high-order, time-stepping methods for solving nonlinear Klein–Gordon equations"
  2. NA2016/02: Jing Gao, Marissa Condon & Arieh Iserles, "Quadrature methods for highly oscillatory singular integral"
  3. NA2016/03: Jing Gao & Arieh Iserles, "Error analysis of the extended Filon-type method for highly oscillatory integrals"
  4. NA2016/04: Jing Gao & Arieh Iserles, "A generalization of Filon–Clenshaw–Curtis quadrature for highly oscillatory integrals"
  5. NA2016/05: Jing Gao & Arieh Iserles, "An adaptive Filon algorithm for highly oscillatory integrals"

2015:

  1. NA2015/01: Alfredo Deaño, Daan Huyberchs & Arieh Iserles, "The kissing polynomials and their Hankel determinants"
  2. NA2015/02: Arieh Iserles, Karolina Kropielnicka & Pranav Singh, "On the discretisation of the semiclassical Schrödinger equation with time-dependent potential"
  3. NA2015/03: Ernst Hairer & Arieh Iserles, "Banded, stable, skew-symmetric differentiation matrices of high order"
  4. NA2015/04: Alberto Gil C.P. Ramos, "Uniform and high-order practical implementation of Sturm–Liouville problems via Fer streamers"
  5. NA2015/05: A, Iserles & Q.R.W. Quispel, "Why geometric numerical integration?"
  6. NA2015/06: Philipp Bader, Arieh Iserles, Karolina Kropielnicka & Pranav Singh, "Efficient methods for time-dependence in semiclassical Schrödinger equations"

2014:

  1. NA2014/01: Alberto Gil C.P. Ramos, "Numerical solution of Sturm–Liouville problems via Fer streamers: Absolutely integrable potentials and self-adjoint boundary conditions"
  2. NA2014/02: M.J.D. Powell, "On fast trust region methods for quadratic models with linear constraints"
  3. NA2014/03: Bin Wang, Arieh Iserles & Xinyuan Wu, "Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems"
  4. NA2014/04: Alberto Gil C.P. Ramos, "Uniform and high-order discretization schemes for Sturm–Liouville problems via Fer streamers"

2013:

  1. NA2013/01: Arieh Iserles, "On skew-symmetric differentiation matrices"
  2. NA2013/02: Arieh Iserles, "Three stories of high oscillation"
  3. NA2013/03: Bin Wang, Arieh Iserles & Xinyuan Wu, "Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems", An updated version of this report is NA2014/03.
  4. NA2013/04: A.S. Fokas, A. Iserles & S.A. Smitheman, "The unified method in polygonal domains via the explicit Fourier transform of Legendre polynomials"
  5. NA2013/05: Arieh Iserles & Carola-Bibiane Schönlieb, "Mathematics of information"
  6. NA2013/06: M.J. Cantero & A. Iserles, "From orthogonal polynomials on the unit circle to functional equations via generating functions"
  7. NA2013/07: M. Condon, A. Iserles & S.P. Nørsett, "Differential equations with general highly oscillatory forcing terms"
  8. NA2013/08: M. Condon, J. Gao & A. Iserles, "Asymptotic solvers for highly oscillatory semi-explicit DAEs"
  9. NA2013/09: Alberto Gil C.P. Ramos & Arieh Iserles, "Numerical solution of Sturm–Liouville problems via Fer streamers"
  10. NA2013/10: Ernst Hairer & Arieh Iserles, "Numerical stability in the presence of variable coefficients"

2012:

  1. NA2012/01: Arieh Iserles, "Numerical analysis"
  2. NA2012/02: Sergio Blanes & Arieh Iserles, "Explicit adaptive symplectic integrators for solving Hamiltonian systems"
  3. NA2012/03: M. Condon, A. Deaño, J. Gao & A. Iserles, "Asymptotic solvers for second-order differential equation systems with multiple frequencies"
  4. NA2012/04: Juan Carlos de los Reyes & Carola-Bibiane Schönlieb, "Image denoising: learning noise distribution via PDE-constrained optimization"
  5. NA2012/05: Philipp Bader, Arieh Iserles, Karolina Kropielnicka & Pranav Singh, "Effective approximation for the linear time-dependent Schrödinger equation"
  6. NA2012/06: M. Condon, A. Deaño & A. Iserles, "Simulation of memristors in presence of high-frequency forcing function"
  7. NA2012/07: B. Adcock, A.C. Hansen & C. Poon, "On optimal wavelet reconstructions from Fourier samples: linearity and universality of the stable sampling rate"
  8. NA2012/08: B. Wang & A. Iserles, "Dirichlet series for dynamical systems of first-order ordinary differential equations"

2011:

  1. NA2011/01: M.J.D. Powell, "On the convergence of trust region algorithms for unconstrained minimization without derivatives"
  2. NA2011/02: B. Adcock & A.C. Hansen, "Generalized sampling and infinite dimensional compressed sensing"
  3. NA2011/03: M. Condon, A. Deaño, A. Iserles & K. Kropielnicka, "Efficient computation of delay differential equations with highly oscillatory terms"
  4. NA2011/04: M.J. Cantero & A. Iserles, "On rapid computation of expansions in ultraspherical polynomials"
  5. NA2011/05: M.J. Cantero & A. Iserles, "On expansions in orthogonal polynomials"
  6. NA2011/06: A. Boettcher, S. Grudsky & A. Iserles, "The Fox–Li operator as a test and a spur for Wiener–Hopf theory"
  7. NA2011/07: M. Condon, A. Deaño & A. Iserles, "A new simulation technique for RF oscillators"
  8. NA2011/08: M.J. Cantero & A. Iserles, "Orthogonal polynomials on the unit circle and functional-differential equations"
  9. NA2011/09: M.J. Cantero & A. Iserles, "On a curious q-hypergeometric identity"
  10. NA2011/10: B. Adcock, A.C. Hansen & C. Poon, "Beyond consistent reconstructions: optimality and sharp bounds for generalized sampling, and application to the uniform resampling problem"
  11. NA2011/11: M. Condon, A. Deaño, J. Gao & A. Iserles, "Asymptotic solvers for ordinary differential equations with multiple frequencies"
  12. NA2011/12: B. Adcock & A.C. Hansen, "Generalized sampling and the stable and accurate reconstruction of piecewise analytic functions from their Fourier coefficients"
  13. NA2011/13: B. Adcock, A.C. Hansen, E. Herrholz & G. Teschke, "Generalized sampling, infinite-dimensional compressed sensing, and semi-random sampling for asymptotically incoherent dictionaries"
  14. NA2011/14: S. Altinbasak, M. Condon, A. Deaño & A. Iserles, "Highly oscillatory diffusion-type equations"
  15. NA2011/15: A. Iserles & K. Kropielnicka, "Effective approximation for linear time-dependent Schrödinger equation", An updated version of this report is NA2012/05.
  16. NA2011/16: M.J.D. Powell, "The Lagrange method and SAO with bounds on the dual variables"
  17. NA2011/17: B. Adcock, A.C. Hansen, E. Herrholz & G. Teschke, "Generalized sampling: extension to frames and inverse and ill-posed problems"